Abel Equations and Generalizations

Part of the Springer Monographs in Mathematics book series (SMM)


In this chapter, Abel’s equation, exponential iteration, associative and commutative equations, trigonometric equations, and systems of equations are treated. Generalizations and connections to information measures are treated. Hilbert, in his famous address to the International Congress of Mathematicians held in Paris in 1900 [372], posed many unsolved problems. The second part of his fifth problem is devoted in general to functional equations and in particular to functional equations treated by Abel, who was the first to treat functional equations systematically. He presented a general method of solving equations of quite general forms. For the most part, he solved functional equations by reducing them to differential equations.


General Solution Functional Equation Shannon Entropy Information Measure Fundamental Equation 


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Copyright information

© Springer-Verlag US 2009

Authors and Affiliations

  1. 1.Department of Pure MathematicsUniversity of WaterlooWaterloo ONCanada

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